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A mass is placed on a frictionless incline and attached to a pulley by a light string. The situation is sketched below.
The incline angle, theta, is 42.0°, the mass is 3.00 kg, the moment of inertia of the pulley is 0.400 kgm2 and the radius of the pulley is 0.145 m. The mass is released from rest.
(a) What is the magnitude of the acceleration of the mass?
___________m/s2
(b) What is the magnitude of the angular acceleration of the pulley?
___________rad/s2
(c) What is the tension in the string?
___________ N
Attempt
T =tension in the string which opposes mass
weight perpendicular to ramp = mgsinθ
a= linear acceleration
mgsinθT=ma
Iα=T*r(Because force on pulley is tension T and distance from center of pulley is r)
α=a/r
T=Iα/r=Ia/r2
substituting in
mgsinθIa/r2=ma
mgsinθ=a(m+I/r2)
a=mgsinθ/(m+I/r2)=0.8931m/s2
b)α=0.9/0.145=6.1599rad/s2
c)T=Ia/r2=0.4*0.9/(0.145)2=17N
can someone who knows what they are doing look this over and fix any mistakes.
Please i really need this.
The incline angle, theta, is 42.0°, the mass is 3.00 kg, the moment of inertia of the pulley is 0.400 kgm2 and the radius of the pulley is 0.145 m. The mass is released from rest.
(a) What is the magnitude of the acceleration of the mass?
___________m/s2
(b) What is the magnitude of the angular acceleration of the pulley?
___________rad/s2
(c) What is the tension in the string?
___________ N
Attempt
T =tension in the string which opposes mass
weight perpendicular to ramp = mgsinθ
a= linear acceleration
mgsinθT=ma
Iα=T*r(Because force on pulley is tension T and distance from center of pulley is r)
α=a/r
T=Iα/r=Ia/r2
substituting in
mgsinθIa/r2=ma
mgsinθ=a(m+I/r2)
a=mgsinθ/(m+I/r2)=0.8931m/s2
b)α=0.9/0.145=6.1599rad/s2
c)T=Ia/r2=0.4*0.9/(0.145)2=17N
can someone who knows what they are doing look this over and fix any mistakes.
Please i really need this.
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